Resolution | Edmund Optics

Dividing the number of horizontal or vertical pixels on a sensor into the size of the object one wishes to observe will indicate how much space each pixel ... HowmayIhelpyou? Engineersareavailabletoassist. Ouroperatorsarenotavailableatthemoment.Pleaseleaveamessageandwewillcontactyousoon Leaveamessage HappyHolidaysfromEdmundOptics!Pleasenoteourspecialopeninghours.      CHAT    EMAIL Country/Region Wehavesetyourcountry/regiontoUnitedStates Youcanchangethisselectionatanytime,butproductsinyourcart,savedlists,orquotemayberemovediftheyareunavailableinthenewshippingcountry/region. 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Welcome! MyAccount AccessDashboard MyProfile UpdateMyProfile Payment&Shipping AddressBook, TaxCertificates WebOrders ViewPastOrders SavedLists SavedItemsforLater LogOut    Products Capabilities KnowledgeCenter Company ContactUs  MyAccount  Cart   hasbeenaddedtoyourcart. OrderNumberhasbeenaddedtoyourcart. Allitemshavebeenaddedtoyourcart. hasbeenaddedtoyourcomparelist. Productaddedtocart KnowledgeCenter /ApplicationNotes /Imaging /Resolution Resolution http://www.edmundoptics.com/knowledge-center/application-notes/imaging/resolution/ EdmundOpticsInc. http://www.edmundoptics.com Resolution Authors: GregoryHollows, NicholasJames ThisisSection2.2 oftheImagingResourceGuide. PreviousSectionNextSection Resolutionisanimagingsystem’sabilitytoreproduceobjectdetail.Itcanbeinfluencedbyfactorssuchasthetypeoflightingused,thesensorpixelsize,andthecapabilitiesoftheoptics.Thesmallertheobjectdetail,thehighertherequiredresolution. Dividingthenumberofhorizontalorverticalpixelsonasensorintothesizeoftheobjectonewishestoobservewillindicatehowmuchspaceeachpixelcoversontheobjectandcanbeusedtoestimateresolution.However,thisdoesnottrulydetermineiftheinformationonthepixelisdistinguishablefromtheinformationonanyotherpixel. Itisimportanttounderstandwhatcanlimitsystemresolution.Figure1showsapairofsquaresonawhitebackground.Ifthesquaresareimagedontoneighboringpixelsonthecamerasensor,theywillappeartobeonelargerrectangle(a),ratherthantwoseparatesquares(b).Todistinguishthesquares,atleastonepixelmustbebetweenthem.Thisminimumdistanceisthelimitingresolutionofthesystem.Theabsolutelimitationisdefinedbythesizeofthepixelsonthesensorandnumberofpixelsonthesensor.  Figure1:Resolvingtwosquares.Ifthespacebetweenthesquaresistoosmall(a)thecamerasensorwillbeunabletoresolvethemasseparateobjects. TheLinePairandSensorLimitations Resolutionisoftenreportedasadimension.Thisconceptofresolutionbeingaminimumsizethatisresolvablebyalensorsystemisnotacompletedescriptionofresolution.Resolutionismoreaccuratelydescribed asafrequency,measuredinlinepairspermillimeter$\left[\small{\tfrac{\text{lp}}{\text{mm}}}\right]$.Alinepairisapairofblackandwhitesquaresinobjectspace.Lensresolutionisunfortunatelynotabsolute.Atagivenresolution,the abilitytoseethetwosquaresasseparateentitieswillbedependentongreyscalelevel.Asystemcanmoreeasilyresolvealinepairifthedifferenceinthegreyscalesofthesquaresandspacebetweenthem isgreater(Figure1b).Thisgreyscaledifferenceisknownascontrast.Resolutionisthusdefinedasaspatialfrequency,givenin$\left[\small{\tfrac{\text{lp}}{\text{mm}}}\right]$,atwhichaspecificcontrastisachieved. Contrastissetbyconventionfordifferentlensandcameramanufacturersbutisusuallyspecifiedforlensestobe20%.Forthisreason,calculatingresolutionintermsof $\left[\small{\tfrac{\text{lp}}{\text{mm}}}\right]$isextremelyusefulwhencomparinglensesandfordeterminingthebestchoiceforgivensensorsandapplications(formoreinformation,readContrast).  Thesensoriswherethesystemresolutioncalculationbegins.Bystartingwiththesensor,itiseasiertodeterminethelensperformancerequiredtomatchthesensororotherapplicationrequirements.Thehighestfrequencyresolvablebyasensor,theNyquistfrequency,iseffectivelytwopixelsoronelinepair.Table1showstheNyquistlimitassociatedwithpixelsizesfoundonsomecommonsensors.Theresolutionofthesensor$\left(\xi_{\small{\text{Sensor}}}\right)$,referredtoasthesystem’simagespaceresolution$\left(\xi_{\small{\text{ImageSpace}}}\right)$,iscalculatedbymultiplyingthepixelsize(s),usuallyinunitsofmicrons,by2(tocreateapair),anddividingthatinto1000toconverttomm: (1)$$\xi_{\small{\text{Sensor}}}=\xi_{\small{\text{ImageSpace}}}=\left(\frac{1}{2\timess}\right)\times\left(\frac{1000 \large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}}{1\text{mm}}\right)$$ (1) $$\xi_{\small{\text{Sensor}}}=\xi_{\small{\text{ImageSpace}}}=\left(\frac{1}{2\timess}\right)\times\left(\frac{1000 \large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}}{1\text{mm}}\right)$$ Sensorswithlargerpixelswillhavelowerlimitingresolutions.Sensorswithsmallerpixelswillhavehigherlimitingresolutions.HowthisinformationisusedtodeterminenecessarylensperformancecanbefoundinSensorPerformanceandLimitations.Thelimitingresolutionontheobjecttobeviewedcanbecalculatedusingtherelationshipsbetweenthesensorsize,thefieldofview(FOV),andthenumberofpixelsonthesensor. Sensorsizereferstothesizeofacamerasensor’sactivearea,specifiedbythesensorformatsize(moreinformationonsensorformatcanbefoundinSensors).However,theexactsensorproportionswillvarydependingontheaspectratio,sothenominalsensorformatsshouldbeusedonlyasaguideline,especiallyfortelecentriclensesandhighmagnificationobjectives.Thesensorsize(H);horizontal,vertical,ordiagonal;canbedirectlycalculatedfromthepixelsizeandnumberofactivepixelsonthesensor(p). (2)$$H=s\timesp\times\left(\frac{1\text{mm}}{1000\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}}\right)$$ (2) $$H=s\timesp\times\left(\frac{1\text{mm}}{1000\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}}\right)$$ PixelSize(µm)AssociatedNyquistLimit$\left(\tfrac{\text{lp}}{\text{mm}}\right)$ 1.67 299.4 2.2 227.3 3.45 144.9 4.54 110.1 5.5 90.9 Table1:Aspixelsizeincreases,theassociatedNyquistlimitin$\left[\small{\tfrac{\text{lp}}{\text{mm}}}\right]$decreasesproportionally. ObjectSpaceResolution Todeterminetheabsoluteminimumresolvablespotviewableontheobject,theratiooftheFOVtothesensorsizemustbecalculated.Thisisalsoknownasthesystemmagnification. (3)$$m=\frac{H}{\text{FOV}}$$ (3) $$m=\frac{H}{\text{FOV}}$$ Systemmagnificationscalestheimagespaceresolutionuptotheobjectspaceresolution$\left(\xi_{\small{\text{ObjectSpace}}}\right)$. (4)$$\xi_{\small{\text{ObjectSpace}}}=\xi_{\small{\text{ImageSpace}}}\timesm$$ (4) $$\xi_{\small{\text{ObjectSpace}}}=\xi_{\small{\text{ImageSpace}}}\timesm$$ Whendevelopinganapplication,asystem’sobjectspaceresolutionistypicallyspecifiedasalengthdimension,ratherthanin$\left[\small{\tfrac{\text{lp}}{\text{mm}}}\right]$.Therearetwowaystomakethisconversion: (5)$$\xi_{\small{\text{ObjectSpace}}}\left[\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}\right]=\left(\frac{1}{2\times\xi_{\small{\text{ObjectSpace}}}\left[\tfrac{\text{lp}}{\text{mm}}\right]}\right)\times\left(\frac{1000\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}}{1\text{mm}}\right)$$ (5) $$\xi_{\small{\text{ObjectSpace}}}\left[\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}\right]=\left(\frac{1}{2\times\xi_{\small{\text{ObjectSpace}}}\left[\tfrac{\text{lp}}{\text{mm}}\right]}\right)\times\left(\frac{1000\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}}{1\text{mm}}\right)$$ (6)$$\xi_{\small{\text{ObjectSpace}}}\left[\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}\right]=\frac{s}{m}$$ (6) $$\xi_{\small{\text{ObjectSpace}}}\left[\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}\right]=\frac{s}{m}$$ Whileitiseasytojumptothelimitingresolutionontheobjectbyusingthelastformula,itisveryusefultodeterminetheimagingspaceresolutionandmagnificationtosimplifylensselection.Itisalsoimportanttonotethattherearemanyadditionalfactorsinvolved,andthislimitationisoftenmuchlowerthanwhatcanbeeasilycalculatedusingtheequations.LearnmoreaboutcontrastlimitationsandlensselectioninContrastandTypesofMachineVisionLenses. ResolutionandMagnificationExampleCalculationsUsingaSonyICX625Sensor KnownParameters:PixelSize:3.45×3.45μmNumberofPixels:2448×2050DesiredFOV(Horizontal):100mm LimitingSensorResolution: \begin{align}\xi_{\small{\text{ImageSpace}}}&=\left(\frac{1}{2\timess}\right)\times\left(\frac{1000\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}}{1\text{mm}}\right)\\&=\left(\frac{1}{2\times3.45\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}}\right)\times\left(\frac{1000\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}}{1\text{mm}}\right)\approx145\tfrac{\text{lp}}{\text{mm}}\end{align} SensorDimensions: $$H_{\small{\text{Horizontal}}}=3.45\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}\times2448\times\left(\frac{1\text{mm}}{1000\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}}\right)=8.45\text{mm}$$ $$H_{\small{\text{Vertical}}}=3.45\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}\times2050\times\left(\frac{1\text{mm}}{1000\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}}\right)=7.07\text{mm}$$ Magnification: $$m=\frac{8.56\text{mm}}{100\text{mm}}=0.0845X$$ Resolution: $$\xi_{\small{\text{ObjectSpace}}}\left[\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}\right]=145\tfrac{\text{lp}}{\text{mm}}\times0.0845=12.25\tfrac{\text{lp}}{\text{mm}}\approx41\large{\unicode[CambriaMath]{x03BC}}\normalsize{\text{m}}$$ PreviousSectionNextSection FeaturedResources  ApplicationNote Contrast  ApplicationNote SensorPerformanceandLimitations  ApplicationNote TypesofMachineVisionLenses EdmundOptics®Imaging:ManufacturingCapabilities LearnMore   Wasthiscontentusefultoyou? 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